Tent space well-posedness for parabolic Cauchy problems with rough coefficients

Journal of Differential Equations - Tập 269 - Trang 11086-11164 - 2020
Wiktoria Zatoń1
1Universität Zürich, Institut für Mathematik, Winterthurerstrasse 190, 8057 Zürich, Switzerland

Tài liệu tham khảo

Aronson, 1967, Bounds for the fundamental solution of a parabolic equation, Bull. Am. Math. Soc., 73, 890, 10.1090/S0002-9904-1967-11830-5 Auscher, 2007, On necessary and sufficient conditions for Lp-estimates of Riesz transforms associated to elliptic operators on Rn and related estimates, Mem. Am. Math. Soc., 186 Auscher, 2019, On regularity of weak solutions to linear parabolic systems with measurable coefficients, J. Math. Pures Appl. (9), 121, 216, 10.1016/j.matpur.2018.08.002 Auscher, 2020, L2 well-posedness of boundary value problems for parabolic systems with measurable coefficients, J. Eur. Math. Soc., 22, 2943, 10.4171/JEMS/980 Auscher, 2001, The solution of the Kato square root problem for higher order elliptic operators and systems on Rn, J. Evol. Equ., 1, 361, 10.1007/PL00001377 Auscher, 2012, Singular integral operators on tent spaces, J. Evol. Equ., 12, 741, 10.1007/s00028-012-0152-4 Auscher, 2019, On existence and uniqueness for non-autonomous parabolic Cauchy problems with rough coefficients, Ann. Sc. Norm. Super. Pisa, Cl. Sci. (5), 19, 387 Auscher, 2000, Equivalence between regularity theorems and heat kernel estimates for higher order elliptic operators and systems under divergence form, J. Funct. Anal., 177, 310, 10.1006/jfan.2000.3643 Auscher, 1998, Square root problem for divergence operators and related topics, Astérisque, 249 Barton, 2016, Gradient estimates and the fundamental solution for higher-order elliptic systems with rough coefficients, Manuscr. Math., 151, 375, 10.1007/s00229-016-0839-x Bernicot, 2016, Gaussian heat kernel bounds through elliptic Moser iteration, J. Math. Pures Appl. (9), 106, 995, 10.1016/j.matpur.2016.03.019 Björn, 2011, Nonlinear Potential Theory on Metric Spaces, vol. 17 Blunck, 2005, Generalized Gaussian estimates and the Legendre transform, J. Oper. Theory, 53, 351 Bögelein, 2008, Higher integrability for weak solutions of higher order degenerate parabolic systems, Ann. Acad. Sci. Fenn., Math., 33, 387 Campanato, 1964, Proprietà di una famiglia di spazi funzionali, Ann. Sc. Norm. Super. Pisa (3), 18, 137 Cao, 2016, Maximal function characterizations of Hardy spaces associated to homogeneous higher order elliptic operators, Forum Math., 28, 10.1515/forum-2014-0127 Cherrier, 2012, Linear and Quasi-Linear Evolution Equations in Hilbert Spaces, vol. 135 Coifman, 1985, Some new function spaces and their applications to harmonic analysis, J. Funct. Anal., 62, 304, 10.1016/0022-1236(85)90007-2 Dautray, 1992 Davies, 1995, Uniformly elliptic operators with measurable coefficients, J. Funct. Anal., 132, 141, 10.1006/jfan.1995.1103 de Simon, 1964, Un'applicazione della teoria degli integrali singolari allo studio delle equazioni differenziali lineari astratte del primo ordine, Rend. Semin. Mat. Univ. Padova, 34, 205 Deny, 1954, Les espaces du type de Beppo Levi, Ann. Inst. Fourier (Grenoble), 5, 305, 10.5802/aif.55 Dong, 2011, On the Lp-solvability of higher order parabolic and elliptic systems with BMO coefficients, Arch. Ration. Mech. Anal., 199, 889, 10.1007/s00205-010-0345-3 Fefferman, 1972, Hp spaces of several variables, Acta Math., 129, 137, 10.1007/BF02392215 Giaquinta, 1982, On the partial regularity of weak solutions of nonlinear parabolic systems, Math. Z., 179, 437, 10.1007/BF01215058 Grafakos, 2009, Modern Fourier Analysis, vol. 250 Janson, 1983, Elementary characterisations of Morrey-Campanato spaces, 101 John, 1961, On functions of bounded mean oscillation, Commun. Pure Appl. Math., 14, 415, 10.1002/cpa.3160140317 Kenig, 1993, The Neumann problem for elliptic equations with nonsmooth coefficients, Invent. Math., 113, 447, 10.1007/BF01244315 Koch, 2012, Geometric flows with rough initial data, Asian J. Math., 16, 209, 10.4310/AJM.2012.v16.n2.a3 Koch, 2015, Parabolic equations with rough data, Math. Bohem., 140, 457, 10.21136/MB.2015.144463 Koch, 2001, Well-posedness for the Navier–Stokes equations, Adv. Math., 157, 22, 10.1006/aima.2000.1937 Maz'ya, 2011, Sobolev Spaces with Applications to Elliptic Partial Differential Equations Fundamental, vol. 342 Moser, 1964, A Harnack inequality for parabolic differential equations, Commun. Pure Appl. Math., 17, 101, 10.1002/cpa.3160170106 Nash, 1957, Parabolic equations, Proc. Natl. Acad. Sci. USA, 43, 754, 10.1073/pnas.43.8.754 Šneĭberg, 1974, Spectral properties of linear operators in interpolation families of Banach spaces, Mat. Issled., 9, 214 Solonnikov, 1965, On boundary value problems for linear parabolic systems of differential equations of general form, Tr. Mat. Inst. Steklova, 83 Stein, 1993, Harmonic Analysis: Real-Variable Methods, Orthogonality and Oscillatory Integrals, vol. 43